MinT - Information on Result #940381

Information on Result #940381

Linear OOA(8¹¹⁸, 366, F₈, 2, 45) (dual of [(366, 2), 614, 46]-NRT-code), using trace code based on linear OOA(64⁵⁹, 183, F₆₄, 2, 45) (dual of [(183, 2), 307, 46]-NRT-code), using

constructionÂ X applied to AG(2;F,306P) âŠ‚ AG(2;F,314P) [i] based on
1. linear OOA(64⁵², 176, F₆₄, 2, 45) (dual of [(176, 2), 300, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,306P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64⁴⁴, 176, F₆₄, 2, 37) (dual of [(176, 2), 308, 38]-NRT-code), using algebraic-geometric NRT-code AG(2;F,314P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁷, 7, F₆₄, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁷, 64, F₆₄, 2, 7) (dual of [(64, 2), 121, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;121,64) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹¹⁹, 366, F₈, 2, 45) (dual of [(366, 2), 613, 46]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹¹⁸, 183, F₈, 3, 45) (dual of [(183, 3), 431, 46]-NRT-code)	[i]		OOA Folding